Solving First Degree Equations
First Degree Equation: An equation characterized by having a single variable
... which may be repeated within the equation more than once ... which
is raised to the first power. Note: plain variable "x" is the same as "x1"
... plain variable "x" is the same as "x" raised to the first power.
A typical 1st degree equation is shown below ... together with the normal
steps of solutions:
STEP 1: Eliminate parenthesis (if any) by multiplying through
using the distributive property.
STEP 2: Eliminate fractions (if any) by finding the common
denominator and multiplying the entire equation through by the common denominator.
In this example, "12" is the common denominator. NOTE: Notice that the
negative sign in front of the compound fraction "(5x - 3)/4" must be distributed
through the entire numerator. You are subtracting the total fraction.
STEP 3: Combine like terms (if any) on both the left and right sides
of the equation.
STEP 4: Isolate "x" (or the variable being solved for) to
one side of the equation ... and at the same time get non-"x" terms
to the opposite side. In this example, you'd subtract "10x" from both sides
of the equation (add "-10x" to both sides) ... and subtract "7" from both
sides of the equation.
STEP 5: Get "x" by its lonesome (get the variable all by itself).
In this example, divide both sides of the equation by "5" (or, equivalent,
multiply both sides of the equation by the fraction "1/5".
STEP 6 (optional): Once an answer is produced, it should be able to be
substituted into the original equation ... and make it true. This is a
method that can be used to "check" an answer.
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